The United States hopes to achieve "major disarmament" by North Korea within the next two-and-a-half years, but there will be no sanctions relief before that, according to Secretary of State Mike Pompeo.

Key points:

Mr Pompeo says the initial agreement document did not capture everything that was agreed by the leaders

He said he is confident that the North Koreans understand there will be verification of any denuclearisation actions

But the brief document from the two leaders' historic meeting provided no details on when Pyongyang would give up a nuclear weapons program that has advanced enough to threaten the US, or how the dismantling might be verified.

Mr Pompeo was in Seoul on Wednesday to brief South Korean officials on the summit.

Speaking alongside Japanese and South Korean foreign ministers, Mr Pompeo said there would be no sanctions relief for North Korea until it denuclearises.

"We're going to get denuclearisation," he said.

"Only then will there be relief from the sanctions."

Mr Pompeo is pushing back on a report from North Korean official state media that said Mr Trump and Mr Kim had agreed to a "step-by-step" process.

That was interpreted as meaning the US would grant concessions to North Korea along the way despite longstanding US insistence that it would not.

Mr Pompeo said Mr Trump had been "incredibly clear" about the sequencing of the process.

Asked earlier by reportersif he would like to accomplish major nuclear disarmament within Mr Trump's current term, which ends on January 20, 2021, Mr Pompeo replied:

"Oh yes, most definitively. Absolutely … you used the term major, major disarmament, something like that? We're hopeful that we can achieve that in the two-and-a-half years.

"I am ... confident they understand that there will be in-depth verification."

He added that the initial agreement between Mr Trump and Mr Kim had not captured all of what had been agreed by the two sides.

"Not all of that work appeared in the final document," Mr Pompeo said.

"But lots of other places where there were understandings reached, we couldn't reduce them to writing, so that means there's still some work to do, but there was a great deal of work done that is beyond what was seen in the final document that will be the place that we will begin when we return to our conversations."

The US has long insisted on complete, verifiable and irreversible denuclearisation by North Korea, but in the summit statement, North Korea committed only to the "complete denuclearisation of the Korean Peninsula," phrasing it has used in the past.

North Korea has often rejected unilateral nuclear disarmament, instead referring to the denuclearisation of the peninsula.

That has always been interpreted in part as a call for the US to remove its "nuclear umbrella" protecting South Korea and Japan.

Mr Pompeo bristled at a question about why the words "verifiable" and "irreversible" were not in the summit joint statement, in the context of denuclearisation.

"It's in the statement. You're just wrong about that … because complete encompasses verifiable and irreversible. I suppose you could argue semantics, but let me assure you that it's in the document," Mr Pompeo said.

"Of course it will … I find that question insulting and ridiculous and frankly ludicrous."

Critics in the US said the joint statement by the two leaders was short on detail and that Mr Trump had made too many concessions to Mr Kim, whose country is under UN sanctions for its nuclear and weapons programs and is widely condemned for human rights abuses.

"Adopting the North Korean view on American military exercises, which President Trump did, is nothing short of a public relations coup for Chairman Kim," US Senate Minority Leader Chuck Schumer said in a speech on the Senate floor.

"President Trump agreed to freeze joint military exercises with South Korea. And, he called them provocations: right out of the North Korean propaganda playbook.

"And, it seems President Trump didn't even think it through or consult with anybody.

Mr Pompeo, who is charged by Mr Trump with leading the follow-on negotiations with North Korea, said he hoped that talks would resume quickly.

"I don't know exactly what the timing will be for our next conversation with the North Koreans," Mr Pompeo said.

"I would anticipate it will be fairly quickly after we return to our home countries.

"I don't know exactly what form that will take, but I'm very confident that by some time in the next week or so we will begin the engagement."

North Korea's state media also hailed the summit as a success, including highlighting Mr Trump's surprise announcement after the summit that the United States would stop military exercises with South Korea.